Monodromy conjecture for semi-quasihomogeneous hypersurfaces

TL;DR

This paper proves the monodromy conjecture linking motivic zeta function poles with b-function roots for semi-quasihomogeneous hypersurfaces, extending to twisted forms, advancing understanding in singularity theory.

Contribution

It provides a proof of the monodromy conjecture for semi-quasihomogeneous hypersurfaces, including a novel generalization involving differential form twists.

Findings

Confirmed the monodromy conjecture for semi-quasihomogeneous hypersurfaces

Extended the conjecture to include twisted differential forms

Established connections between motivic zeta functions and b-functions

Abstract

We give a proof the monodromy conjecture relating the poles of motivic zeta functions with roots of b-functions for isolated quasihomogeneous hypersurfaces, and more generally for semi-quasihomogeneous hypersurfaces. We also give a strange generalization allowing a twist by certain differential forms.